Variational Method
This page contains resources about Variational Methods and Variational Bayesian Inference. Subfields and Concepts * Calculus of Variations / Variational Calculus * Free energy * Kullback–Leibler (KL) Divergence * Variational Bayes * Variational Bayesian EM (VBEM) * Laplace Approximation * Expectation Propagation ** Loopy Belief Propagation / Sum-Product Message Passing * Kullback-Leibler Variational Inference / Mean field Variational Bayes ** Structured Mean field / Structured Variational Approximation ** Weighted Mean Field * Tree-based reparameterizations * Tree-reweighted belief propagation * Bethe and Kikuchi free energy Online Courses Video Lectures * Lecture Notes *COS597C: Advanced Methods in Probabilistic Modeling BY David M. Blei Books and Book Chapters * Theodoridis, S. (2015). "Chapter 13: Bayesian Learning: Approximate Inference and Nonparametric Models". Machine Learning: A Bayesian and Optimization Perspective. Academic Press. * Murphy, K. P. (2012). "Chapter 21: Variational inference". Machine Learning: A Probabilistic Perspective. MIT Press. * Barber, D. (2012). "Chapter 11: Learning with Hidden Variables". Bayesian Reasoning and Machine Learning. Cambridge University Press. * Barber, D. (2012). "Chapter 28: Deterministic Approximate Inference". Bayesian Reasoning and Machine Learning. Cambridge University Press. * Koller, D., & Friedman, N. (2009). "Chapter 11: Inference as Optimization". Probabilistic Graphical Models. MIT Press. * Bishop, C. M. (2006). "Chapter 10: Approximate Inference". Pattern Recognition and Machine Learning. Springer. * MacKay, D. J. (2003). "Chapter 33: Variational Methods" Information Theory, Inference and Learning Algorithms. Cambridge University Press. Scholarly Articles * Blei, D. M., Kucukelbir, A., & McAuliffe, J. D. (2016). Variational inference: A review for statisticians. arXiv preprint arXiv:1601.00670. * Archer, E., Park, I. M., Buesing, L., Cunningham, J., & Paninski, L. (2015). Black box variational inference for state space models. arXiv preprint arXiv:1511.07367. * Ranganath, R., Gerrish, S., & Blei, D. M. (2014). Black Box Variational Inference. In AISTATS (pp. 814-822). * Hoffman, M. D., Blei, D. M., Wang, C., & Paisley, J. W. (2013). Stochastic variational inference. Journal of Machine Learning Research, 14(1), 1303-1347. * Fox, C. W., & Roberts, S. J. (2012). A tutorial on variational Bayesian inference. Artificial intelligence review, 38(2), 85-95. * Wainwright, M. J., & Jordan, M. I. (2008). Graphical models, exponential families, and variational inference. Foundations and Trends® in Machine Learning, 1''(1-2), 1-305. * Wainwright, M., & Jordan, M. (2005). A variational principle for graphical models. ''New Directions in Statistical Signal Processing, 155. * Beal, M. J. (2003). Variational algorithms for approximate Bayesian inference. Ph.D. Dissertation, University College London. * Xing, E. P., Jordan, M. I., & Russell, S. (2003). A generalized mean field algorithm for variational inference in exponential families. In Proceedings of the Nineteenth conference on Uncertainty in Artificial Intelligence (pp. 583-591). Morgan Kaufmann Publishers Inc. * Wainwright, M. J., & Jordan, M. I. (2003). Variational inference in graphical models: The view from the marginal polytope. In Proceeding of Annual Allerton Conference of Communication Control and Computing (Vol. 41, No. 2, pp. 961-971). * Lawrence, N. D. (2001). Variational inference in probabilistic models. Ph.D. Dissertation, ''University of Cambridge. * Jordan, M. I., Ghahramani, Z., Jaakkola, T. S., & Saul, L. K. (1999). An introduction to variational methods for graphical models. ''Machine learning,37(2), 183-233. Tutorials *Challenges in Variational Inference: Optimization, Automation, and Accuracy by Rajesh Ranganath - NIPS 2015 *Variational Bayesian inference by Kay H. Brodersen - 2013 *High-Level Explanation of Variational Inference by Jason Eisner - 2011 *Variational Methods by Zubin Gahramani - 2003 *Variational Mean Field for Graphical Models by Baback Moghaddam Software * Vilds - Black box variational inference for state space models in Python * Edward: A library for probabilistic modeling, inference, and criticism - Python with TensorFlow * VIBES See also *Monte Carlo Methods, an other set of methods for Approximate Inference in Graphical Models *Ensemble Learning *Estimation Theory *Information Theory *Convex Optimization Other Resources * Variational-Bayes - A repository of research papers, software, and links related to the use of variational methods for approximate Bayesian learning up to 2003 Category:Probabilistic Graphical Models